Question

Choose the correct linear equation given the slope and a point P.

m=-4, P=(-3,5)

Answer 1

To find the linear equation given the slope and a point, we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point, and \( m \) is the slope. Here, we have:

- \( m = -4 \)
- \( P = (-3, 5) \) which gives \( x_1 = -3 \) and \( y_1 = 5 \)

Substituting these values into the point-slope form:

\[
y - 5 = -4(x - (-3))
\]

This simplifies to:

\[
y - 5 = -4(x + 3)
\]

Now, we can distribute the -4:

\[
y - 5 = -4x - 12
\]

Next, we add 5 to both sides to solve for \( y \):

\[
y = -4x - 12 + 5
\]

\[
y = -4x - 7
\]

Thus, the linear equation is:

\[
\boxed{y = -4x - 7}
\]